Numerical Investigation to Determine Optimal Inline Semi-Circular Cylinder Configurations for Coherent Karman Vortex Streets*

 Recent studies showed that fishes exploit the energy of vortices shed by bluff bodies to swim efficiently. When swimming in such a coherent vortex structure, fish adopt a behavior known as 'Kármán Gait'. Therefore, a fishway could be contrived with a row of cylinders in order to reduce the energy expenditure of fish  and thus favor upstream migration. However, it is unclear, given the diameter, which cylinder spacing to adopt to ensure that counter-rotating vortices interact in a constructive manner and create a coherent vortex street.

In this work, we use computational fluid dynamics to solve the flow around a row of semi-circular cylinders (SCC) with the number of cylinders ranging from 1 to 5. We characterize a coherent vortex street based on the peakedness of the energy spectrum of the spanwise velocity. We employ a state-of-the-art optimization technique to determine the cylinder spacing which maximizes the spectrum peakedness. Our findings show that, in order to generate a coherent vortex street, the SCC should be positioned within a specific range of cylinder spacing values. We further observed that the optimal SCC spacing values for coherent vortex street generation lies within the reattachment vortex shedding regime.